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Simplifying (32 + x)(50 + x) = 2320 Multiply (32 + x) * (50 + x) (32(50 + x) + x(50 + x)) = 2320 ((50 * 32 + x * 32) + x(50 + x)) = 2320 ((1600 + 32x) + x(50 + x)) = 2320 (1600 + 32x + (50 * x + x * x)) = 2320 (1600 + 32x + (50x + x2)) = 2320 Combine like terms: 32x + 50x = 82x (1600 + 82x + x2) = 2320 Solving 1600 + 82x + x2 = 2320 Solving for variable 'x'. Reorder the terms: 1600 + -2320 + 82x + x2 = 2320 + -2320 Combine like terms: 1600 + -2320 = -720 -720 + 82x + x2 = 2320 + -2320 Combine like terms: 2320 + -2320 = 0 -720 + 82x + x2 = 0 Factor a trinomial. (-90 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-90 + -1x)' equal to zero and attempt to solve: Simplifying -90 + -1x = 0 Solving -90 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + -1x = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -1x = 0 + 90 -1x = 0 + 90 Combine like terms: 0 + 90 = 90 -1x = 90 Divide each side by '-1'. x = -90 Simplifying x = -90Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-90, 8}
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